Method and apparatus for determining movement of an object in an imager

ABSTRACT

A method and apparatus for determining the three-dimensional movement of a patient positioned on a table between an X-ray source and an image receiver of an X-ray imaging apparatus. The apparatus has an X-ray source positioned opposite an image receiver, the X-ray source and the image receiver being driven in rotation about an axis. The method and apparatus has the following operation: at least three radio-opaque markers are placed on the patient&#39;s body; at least one first radiographic image of the patient is taken for a first determined fixed position of the imaging apparatus; at least one second radiographic image of the patient is taken for a second determined fixed position of the imaging apparatus; and a matrix of the three-dimensional movement of the patient with respect to the X-ray source of the imaging apparatus is determined on the basis of the two-dimensional movements of the markers in the radiographic images, the X-ray source constituting a fixed reference frame.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of a priority under 35 USC 119(a)-(d) to French Patent Application No. 05 01741 filed Feb. 21, 2005,the entire contents of which are hereby incorporated by reference.

BACKGROUND OF THE INVENTION

An embodiment of the present invention relates to a method and apparatusfor determining the movement of an object in an imager. In particular,an embodiment of the present invention relates to three-dimensionalmovement of a patient positioned on a table between a radiation sourceand an image receiver of an imaging apparatus.

In the field of medical imaging, it is well known to use radio-opaquemarkers positioned on the object, such as a patient, as reference pointsin order to assist the guiding of surgical instruments during anoperation and/or to permit the merging of images, for instance thesuperposition of images acquired by an imaging apparatus. The imagingapparatus conventionally comprises a means for providing a radiationsource, such as X-rays, positioned opposite a means for receiving animage, the means for providing a radiation source and the means forreceiving an image being driven in relative rotation about at least oneaxis, usually three axes, means for operating, means for acquisition,means for visualizing the images and means for control. The patient ispositioned on a table that can be moved in the three possibletranslations associated with a given space, i.e., longitudinally,laterally and vertically, so that the part of the patient's body to beexamined and/or treated extends between the means for providing aradiation source and the means for receiving an image. This mobility ofthe table and the radiation source and the image receiver allows apractitioner to acquire images for any part of the body of a patientlying on the table. For instance, it is customary to use two-dimensionalfluoroscopic images obtained by irradiating the patient with low X-raydoses during an intervention in order to guide the instrument in thepatient's organ to be treated. The information associated with thesefluoroscopic images may preferably be introduced intothree-dimensionally reconstructed images in order to improve the guidingof the surgical instruments. Alternatively, acquired three-dimensionalimages may be projected onto the two-dimensional fluoroscopic imagesacquired during the intervention.

In order to permit these projections of 3D images onto 2D fluoroscopicimages or, conversely, to reposition the 2D fluoroscopic imageinformation in 3D images, it is necessary to determine the acquisitionparameters of the 2D fluoroscopic images placed on the patient's bodyregion to be examined. This is the case, for example, in U.S. Pat. No.6,359,960 that describes a method for automatically determining thethree-dimensional coordinates of markers without the intervention of auser. The method comprises detecting the positions of the markers intwo-dimensional projections then, by an inverse projection, indetermining the coordinates of the markers identified in threedimensions, the geometry of the projections being known.

These methods for determining the three-dimensional coordinates ofmarkers positioned on the patient make it possible to guide surgicalinstruments during an operation and/or to allow merging of images, forinstance projection of 3D images into 2D radiographic images or viceversa; These methods nevertheless assume that the patient remainsperfectly stationary when the three-dimensional coordinates of themarkers are being determined. It is very common for the patient to moveduring the procedure, however, leading to inaccuracy in the projectionsof the 3D images into the radiographic images, or vice versa, which maylead to an interpretation error of the visualized images.

BRIEF DESCRIPTION OF THE INVENTION

An embodiment of the invention overcomes this drawback by providing amethod and apparatus for determining the three-dimensional movement of apatient positioned on a table between an X-ray source and an imagereceiver of an X-ray imaging device, in order to adjust the projectionof a three-dimensionally image of the patient's body onto radiographicimages and/or to reposition two-dimensional fluoroscopic imageinformation in three-dimensionally reconstructed images displayed on themeans for visualization of the imaging apparatus.

An embodiment of the invention relates to a method and apparatus fordetermining the three-dimensional movement of an object positioned onmeans for support between a means for providing a radiation source andmeans for receiving an image, the means for providing a radiation sourcepositioned opposite the means for receiving an image, the means forproviding a radiation source and the means for receiving an image beingdriven in relative in rotation about at least one axis, means foroperating, means for acquisition, means for visualizing the images andmeans for control.

An embodiment of the method and apparatus relates to the determinationof the three-dimensional movement of an object positioned on a means forsupport between a means for providing a radiation source and a means forreceiving an image in an imaging apparatus. The method and apparatus inparticular relates to placing a plurality of markers, at least threeradio-opaque markers, on a body of the object, the markers constitutinga fixed reference frame. Taking or acquiring at least one firstradiographic image of the object for a first determined fixed positionof the imaging apparatus in the reference frame of the markers. Takingor acquiring at least one second radiographic image of the object for asecond determined fixed position of the imaging apparatus in thereference frame of the markers. Determining a matrix of thethree-dimensional movement of the object with respect to the means forproviding a radiation source of the imaging apparatus on the basis ofthe two-dimensional movements of the markers in the radiographic images,the means for providing a radiation source constituting a fixedreference frame.

BRIEF DESCRIPTION OF THE DRAWINGS

Other advantages and characteristics will be understood more clearlyfrom the following description of several alternative embodiments, givenby way of non-limiting examples, of the method on the basis of theappended drawings in which:

FIG. 1 is a schematic perspective view of an embodiment of an imagingapparatus;

FIG. 2 is a perspective view of the head of a patient wearing a supportheadpiece carrying radio-opaque markers;

FIG. 3 is a schematic perspective view of the movement of theprojections of the markers on an image receiver from a first position toa second position;

FIG. 4 is a schematic perspective view of the movement of theprojections of the markers on the image receiver and of a radiationsource according to a homography induced by the plane of the markersconstituting a fixed reference frame; and

FIG. 5 is a schematic representation of a method for generating aradiographic image.

DETAILED DESCRIPTION OF THE INVENTION

Referring to FIG. 1, an imaging apparatus 1 conventionally comprisesmeans for receiving an image 2 (such as a digital image receiver), meansfor providing a radiation 3, such as X-ray, emitting radiation onto themeans for receiving an image 2, the means for receiving an image 2 andthe means for providing a radiation source 3 being respectivelypositioned at the end of a C-shaped or U-shaped arm 4. Arm 4 pivotsabout three axes 5, 5′ and 5″, which are schematically represented bydots and dashes. The C-shaped arm 4 pivots about an axis 5 secured to acarriage 6 a that slides along an intermediate arm 6 b. Intermediate arm6 b can pivot about a second axis 5′ perpendicular to a face of anL-shaped base 6 c, which can pivot about a vertical axis 5″ by means ofa rotary linkage. The C-shaped arm 4 can therefore pivot about threeaxes 5, 5′ and 5″, the axes forming a reference system for a specificposition of the C-shaped arm 4. A position of the C-shaped arm 4 canthus be expressed in the reference system defined by these three axes 5,5′ and 5″ at a position determined by three angles L, P and C, which theC-shaped arm 4 respectively forms with the axes 5, 5′ and 5″. SID willbe used to denote the distance separating the means for providing aradiation source 3 from the means for receiving an image 2, the distanceSID varying according to the position of the C-shaped arm 4 in view ofits mechanical deformation.

The imager apparatus 1 furthermore comprises an adjustable collimator 7positioned at the exit of the means for providing a radiation source 3.The imaging apparatus 1 also comprises means for operating 8 connectedto the means for providing a radiation source 3, to the collimator 7, tothe means for receiving an image 2, to means for acquisition 9 and tomeans for visualization 10. The means for control 11 can be a keyboard,a mouse, control buttons or the like, are connected to the means foroperating 8.

An object, such as patient P, is disposed on a means for support 12,such as a table, extending between the means for providing a radiationsource 3 and the means for receiving an image 2. In order to determinethe three-dimensional movement of the object, the object is fitted witha headpiece 13, as represented in FIG. 2, the headpiece havingradio-opaque markers 14. The markers extend in the same plane on arectangular support 15 extending over the forehead of the patient P. Itwill be noted that the table 12 can be moved in the three possibletranslations associated with a given space, i.e., longitudinally,laterally and vertically, so as to allow a practitioner to acquireimages for any part of the body of a patient lying on the table 12. Atleast one first radiographic image of the patient is taken for a firstdetermined fixed position of the imaging device on which the markers 14appear, without the patient having moved, and a second radiographicimage of the patient is taken for a second determined fixed position ofthe imaging device on which the markers 14 appear, the patient havingmoved with respect to their position when the first radiographic imagewas taken. The matrix of the three-dimensional movement of the patientwith respect to the radiation source is then determined on the basis ofthe two-dimensional movements of the markers 14 in the radiographicimages, the radiation source constituting a fixed reference frame. Thethree-dimensional movement M=(R/T) of the markers 14, i.e., of thepatient, is equivalent to the inverse movement M⁻¹ of the radiationsource 3, as represented in FIG. 3, or planes containing theradiographic images if the markers are assumed to be fixed in space. Theterm movement of the markers 14 is intended to mean a rigidthree-dimensional movement, i.e., the distances separating the markersremain unchanged during their movement. Referring to FIG. 3, themovement of the markers 14 from a first position represented by crosses,to a second position where the markers 14 are represented by squares,corresponds to a movement of the radiation source 3 as indicated by thearrow a.

Considering on the one hand P₁=I₁*E₁, the projection matrixcorresponding to the position of the imaging apparatus when theradiographic image is taken in the first position of the imagingapparatus, I₁ being the matrix of the intrinsic parameters of theimaging apparatus in its first position and E₁ being the matrix of theextrinsic parameters of the imaging apparatus in its first position,where the patient has not moved, and on the other hand P₂=I₂*E₂, theprojection matrix corresponding to the position of the imaging apparatuswhen the radiographic image is taken in the second position of theimaging apparatus, where the patient has moved with respect to theposition when the first radiographic image was acquired, I₂ being thematrix of the intrinsic parameters of the imaging apparatus in itssecond position and E₂ being the matrix of the extrinsic parameters ofthe imaging apparatus in its second position, the movement M can bewritten in the form M=(R/T)=E₁ ⁻¹*E₂. The movement M of the markers isthus equivalent to the movement of the extrinsic parameters betweenposition 1 and position 2 of the imaging apparatus 1 in the fixedreference frame of the markers 14. In order to determine the patient'smovement M, therefore, the matrix of the intrinsic parameters I₁ of theimaging apparatus when taking the first radiographic image and thematrix of the intrinsic parameters I₂ of the imaging apparatus whentaking the second radiographic image are determined, the intrinsicparameters I₁ and I₂ being determined beforehand by any suitable method,for example a multi-image calibration method, and being equal. Thematrix of the extrinsic parameters E₂ of the imaging apparatus whentaking the second radiographic image is then determined, as a functionof the matrix of the intrinsic parameters I₁ of the imaging apparatuswhen taking the first radiographic image. The inverse matrix of theextrinsic parameters E₁ ⁻¹of the imaging apparatus is subsequentlydetermined on the basis of the intrinsic parameters I₁, then the matrixM corresponding to the patient's three-dimensional movement isdetermined as a function of the inverse matrix E₁ ⁻¹ of the extrinsicparameters E₁ of the imaging apparatus when taking the firstradiographic image and the matrix of the extrinsic parameters E₂ of theimaging apparatus when taking the second radiographic image.

According to a first alternative embodiment of the method, the extrinsicparameters E₂ are estimated using the intrinsic parameters I₁ of theimaging apparatus in its first position, by minimizing the followingcriterion:$E_{2} = {\arg\quad{\min( {\sum\limits_{i}{{dist}( {\begin{pmatrix}{\hat{X}}^{i} \\{\hat{Y}}^{i}\end{pmatrix} - \begin{pmatrix}X_{2}^{i} \\Y_{2}^{i}\end{pmatrix}} )}} )}}$in which $\begin{pmatrix}{\hat{X}}^{i} \\{\hat{Y}}^{i}\end{pmatrix} = {I*{E_{2}\begin{pmatrix}X_{marker} \\Y_{marker} \\Z_{marker}\end{pmatrix}}}$are the three-dimensional positions projected into theimage by the projection matrix I*E₂, and $ ( \begin{matrix}X_{2}^{i} \\Y_{2}^{i}\end{matrix}\quad  )$are the two-dimensional positions of the markers observed in the secondradiographic image. After having estimated the extrinsic parameters E₂,the movement M of the markers 14 i.e., the patient's movement M isextracted from the first equation.

The matrix of the intrinsic parameters I₁ of the imaging apparatus 1when taking the first radiographic image is determined according to aso-called multi-image calibration method by placing a 3D phantom ofknown geometry between the radiation source 3 and the image receiver 2,then by taking n images of the 3D phantom in the determined fixedposition of the imaging apparatus 1, where n is a positive integer ofthe order of 30, the 3D phantom being moved in rotation and/ortranslation between two successive images. The 3D phantom includesradio-opaque elements and may, for example, have a helical shaped asdescribed in U.S. Pat. No. 5,442,674.

Thus, in order to determine the intrinsic parameters of the imagingapparatus in a determined fixed position, n images are acquired then then projection matrices corresponding to the n images are calculated. Theimaging apparatus 1 remains fixed during the acquisition of the nradiographic images, the intrinsic parameters are identical for all theimages. Furthermore, since the 3D phantom is moved during theacquisition of the n images, the intrinsic parameters are different foreach of the n images. It is then expedient to minimize an error functionbased on the projection of the errors calculated with n images,corresponding to the determined fixed position of the imaging apparatus1 according to the equation E=argmin(f(u₀,v₀,α,R₁,T₁,R₂,T₂, . . . ,R_(n),T_(n))) in which uo, vo and α are the three intrinsic parametersof the imaging apparatus 1 and R_(i) and T_(i) are the extrinsicparameters for image number i, in order to determine the intrinsicparameters of the imaging apparatus in its determined fixed position.

The error function can be written in the form:$f = {\sum\limits_{i = 1}^{n}{\sum\limits_{j = 1}{{dist}( {\begin{pmatrix}{\hat{X}}^{j} \\{\hat{Y}}^{j}\end{pmatrix} - \begin{pmatrix}X_{2}^{j} \\Y_{2}^{j}\end{pmatrix}} )}}}$with $ ( \begin{matrix}X_{2}^{j} \\Y_{2}^{j}\end{matrix}\quad  )$being the two-dimensional positions of the markers observed in imagenumber i, and the relation $\begin{pmatrix}{\hat{X}}^{j} \\{\hat{Y}}^{j}\end{pmatrix} = {M_{i}\begin{pmatrix}X_{marker} \\Y_{marker} \\Z_{marker}\end{pmatrix}}$in which $ ( \begin{matrix}X_{marker} \\Y_{marker} \\Z_{marker}\end{matrix}\quad  )$are the three-dimensional positions projected into the image by theprojection matrix M_(i), and $M_{i} = {\begin{bmatrix}f & 0 & u_{0} \\0 & f & v_{0} \\0 & 0 & 1\end{bmatrix}\begin{bmatrix}\quad & \quad & \quad \\\quad & R_{i} & T_{i} \\\quad & \quad & \quad\end{bmatrix}}$is the projection matrix for image number i.

According to a second alternative embodiment of the method, the matrixof the extrinsic parameters E₂ of the imaging apparatus when taking thesecond radiographic image is determined by calculating the planarhomography H, i.e., the homography with respect to a plane π, betweenthe first radiographic image of the markers 14 forming a plane P₁ andthe second radiographic image of the markers 14 forming a second planeP₂, as schematically represented in FIG. 4. According to this homographyH, the radiation source 2 moves when considering the fixed referenceframe of the markers 14. Since the markers 14 extend in the same planeπ, a planar homography H can thus be assigned between the plane P₁ ofthe first radiographic image and the plane P₂ of the second radiographicimage; which can be written in the form X2∝HX₁ for all the markers 14 ofthe plane π, in which ∝ describes an equality involving a multiplicativefactor.

Considering L, the three-dimensional movement between thethree-dimensional coordinate system and the coordinate system in whichthe equation of the plane π is y=0, we have the following for all themarkers 14 of the plane π: X ₁=<P_(i)L>*(x z 1)^(t) in which <A>describes the matrix A without its second column. <P_(i)L>is invertibleunless the plane π passes through the origin of the radiation source 3.It follows from the previous two equations that <P₂L>∝H<P₁L>. Thesuppression of the second column of the matrix P₂ does not prevent thecomplete three-dimensional movement M of the markers 14 from beingfound. In view of the preceding equation, we know <P₂L> and, since I isequal to I₁ and I₂ as seen above, we obtain the following equation:Γ⁻¹H<P₁L>∝[r₁ r₃ t] in which r₁ and r₂ are orthogonal vectors. Thesecond column of the movement of the markers is simply given byr₂=r₃×r₁. This orthogonality condition is never perfectly satisfied inpractice, and a renormalization should preferably be applied. It is thenpossible to calculate E₂ and M from the following to equations:E ₂=[r₁ r₂ r₃ t]*L ⁻¹ and M=E ₁ ⁻¹ *E ₂.

It will be noted that one or other of the methods described above can beused to estimate the three-dimensional movement of the markers 14, thechoice of method depending on the distribution of the markers 14 in theimage.

The method for determining the three-dimensional movement of a patientpositioned on a table 12 between a radiation source 3 and an imagereceiver 2 of an imaging apparatus 1 is employed for adjusting theprojection of a three-dimensionally reconstructed image of the patient'sbody onto radiographic images, or for repositioning two-dimensionalradiographic image information in a three-dimensionally reconstructedimage, which are displayed on the means for visualization 10 in order toassist the guiding of an object in an organ of the patient. Referring toFIG. 5, the 2D detection 101 of the radio-opaque markers makes itpossible to deduce the patient's movement M 102. A computer programrecorded in the means for operating 8 of the imaging apparatus 1constructs a visualized image 103 by means of a projection matrix 104 onthe basis of the patient's movement M 102, a radiographic image 105 anda three-dimensional image 106 of an organ of the patient, the visualizedimage 103 being the projection of a three-dimensional image of thepatient's body onto radiographic images, or vice versa.

It is apparent that the markers 14 may be placed directly on thepatient's body, at least three markers 14 forming a plane beingdesirable.

An embodiment of the method comprises: placing at least threeradio-opaque markers on the body of the object, the markers constitutinga fixed reference frame; taking at least one first radiographic image ofthe object for a first determined fixed position of the imagingapparatus in the reference frame of the markers; taking at least onesecond radiographic image of the object for a second determined fixedposition of the imaging apparatus in the reference frame of the markers;determining the matrix of the three-dimensional movement of the objectwith respect to the means for providing a radiation source of theimaging apparatus on the basis of the two-dimensional movements of themarkers in the radiographic images, the means for providing a radiationsource then constituting a fixed reference frame.

In order to determine the patient's three-dimensional movement matrixwith respect to the radiation source of the imaging apparatus on thebasis of the two-dimensional movements of the markers in theradiographic images: the matrix of the intrinsic parameters of theimaging device is determined; the matrix of the extrinsic parameters ofthe imaging apparatus in the second position is determined as a functionof the matrix of the intrinsic parameters of the imaging apparatus; theinverse matrix of the extrinsic parameters of the imaging apparatus inits first position is determined; the matrix corresponding to thethree-dimensional movement of the object is determined as a function ofthe inverse matrix of the extrinsic parameters of the imaging apparatusin its first position in the fixed reference frame of the markers andthe matrix of the extrinsic parameters of the imaging apparatus in itssecond position in the fixed reference frame of the markers.

According to the first alternative embodiment of the method, the matrixof the extrinsic parameters of the imaging apparatus when taking thesecond radiographic apparatus is determined as a function of the matrixof the intrinsic parameters of the imaging apparatus when taking thefirst radiographic image in the fixed reference frame of the markers.

According to the second alternative embodiment of the method, the matrixof the extrinsic parameters of the imaging apparatus when taking thesecond radiographic image is determined by calculating the planarhomography H between the first radiographic image of the markers and thesecond radiographic image of the markers, the markers forming a fixedreference frame.

The markers can be either placed directly on the patient's body or aresecured to a support placed on the patient's body.

The matrix and the inverse matrix of the extrinsic parameters of theimaging apparatus in its first position are determined on the basis ofthe matrix of the intrinsic parameters of the imaging apparatus.

The following steps can be used to determine the intrinsic parameters ofthe imaging device: a 3D phantom is placed between the radiation sourceand the image receiver; a plurality of images of the 3D phantom areacquired in the determined fixed position of the imaging apparatus; the3D phantom being moved in rotation and/or translation between twosuccessive images; and the intrinsic parameters of the imaging apparatusin its fixed position are calculated by performing a calibration on thebasis of the images of the 3D phantom.

The method for determining the three-dimensional movement of an objectpositioned on a means for support between a radiation source and animage receiver of an imaging apparatus provides for adjusting theprojection of a three-dimensionally reconstructed image of the object'sbody onto radiographic images, or in repositioning two-dimensionalradiographic image information in three-dimensionally reconstructedimages displayed on the means for visualization in order to assist theguiding of an object in or into an organ of the patient.

In addition, while an embodiment of the invention has been describedwith reference to exemplary embodiments, it will be understood by thoseskilled in the art that various changes may be made in the functionand/or way and/or result and equivalents may be substituted for elementsthereof without departing from the scope and extent of the invention. Inaddition, many modifications may be made to adapt a particular situationor material to the teachings of the invention without departing from theessential scope thereof. Therefore, it is intended that the inventionnot be limited to the particular embodiment disclosed as the best modecontemplated for carrying out this invention, but that the inventionwill include all embodiments falling within the scope of the appendedclaims. Moreover, the use of the terms first, second, etc. or steps donot denote any order or importance, but rather the terms first, second,etc. or steps are used to distinguish one element or feature fromanother. Furthermore, the use of the terms a, an, etc. do not denote alimitation of quantity, but rather denote the presence of at least oneof the referenced element or feature.

1. A method for determining the three-dimensional movement of an objectpositioned on a means for support between a means for providing aradiation source and a means for receiving an image in an imagingapparatus comprising: placing a plurality of radio-opaque markers on abody of the object, the markers constituting a fixed reference frame;taking at least one first radiographic image of the object for a firstdetermined fixed position of the imaging apparatus in the referenceframe of the markers; taking at least one second radiographic image ofthe object for a second determined fixed position of the imagingapparatus in the reference frame of the markers; and determining amatrix of the three-dimensional movement of the object with respect tothe means for providing a radiation source of the imaging apparatus onthe basis of the two-dimensional movements of the markers in theradiographic images, the means for providing a radiation sourceconstituting a fixed reference frame.
 2. The method according to claim 1comprising: determining a matrix of the intrinsic parameters of theimaging apparatus; determining a matrix of the extrinsic parameters ofthe imaging apparatus in the second position as a function of the matrixof the intrinsic parameters of the imaging apparatus; determining aninverse matrix of the extrinsic parameters of the imaging apparatus inits first position; and determining a matrix corresponding to thethree-dimensional movement of the object as a function of the inversematrix of the extrinsic parameters of the imaging apparatus in its firstposition in the fixed reference frame of the markers and the matrix ofthe extrinsic parameters of the imaging apparatus in its second positionin the fixed reference frame of the markers.
 3. The method according toclaim 2 comprising determining the matrix of the extrinsic parameters ofthe imaging apparatus when taking the second radiographic image as afunction of the matrix of the intrinsic parameters of the imagingapparatus when taking the first radiographic image in the fixedreference frame of the markers.
 4. The method according to claim 2comprising determining the matrix of the extrinsic parameters of theimaging apparatus when taking the second radiographic image bycalculating the planar homography between the first radiographic imageof the markers and the second radiographic image of the markers, themarkers forming a fixed reference frame.
 5. The method according toclaim 1 comprising determining the matrix and the inverse matrix of theextrinsic parameters of the imaging apparatus in its first position onthe basis of the matrix of the intrinsic parameters of the imagingapparatus.
 6. The method according to claim 2 comprising determining thematrix and the inverse matrix of the extrinsic parameters of the imagingapparatus in its first position on the basis of the matrix of theintrinsic parameters of the imaging apparatus.
 7. The method accordingto claim 3 comprising determining the matrix and the inverse matrix ofthe extrinsic parameters of the imaging apparatus in its first positionon the basis of the matrix of the intrinsic parameters of the imagingapparatus.
 8. The method according to claim 4 comprising determining thematrix and the inverse matrix of the extrinsic parameters of the imagingapparatus in its first position on the basis of the matrix of theintrinsic parameters of the imaging apparatus.
 9. The method accordingto claim 1 comprising placing the markers directly on the body of theobject.
 10. The method according to claim 2 comprising placing themarkers directly on the body of the object.
 11. The method according toclaim 3 comprising placing the markers directly on the body of theobject.
 12. The method according to claim 4 comprising placing themarkers directly on the body of the object.
 13. The method according toclaim 5 comprising placing the markers directly on the body of theobject.
 14. The method according to claim 1 comprising placing themarkers directly on the body of the object.
 15. The method according toclaim 2 comprising placing the markers directly on the body of theobject.
 16. The method according to claim 3 comprising placing themarkers directly on the body of the object.
 17. The method according toclaim 4 comprising placing the markers directly on the body of theobject.
 18. The method according to claim 5 comprising placing themarkers directly on the body of the object.
 19. The method according toclaim 2 comprising determining the intrinsic parameters of the imagingapparatus by: placing a 3D phantom between the means for providing aradiation source and the means for receiving an image; acquiring aplurality of images of the 3D phantom in the determined fixed positionof the imaging apparatus, the 3D phantom being moved in rotation and/ortranslation between two successive images; and calculating the intrinsicparameters of the imaging apparatus in its fixed position by performinga calibration on the basis of the images of the 3D phantom.
 20. Themethod according to claim 3 comprising determining the intrinsicparameters of the imaging apparatus by: placing a 3D phantom between themeans for providing a radiation source and the means for receiving animage; acquiring a plurality of images of the 3D phantom in thedetermined fixed position of the imaging apparatus, the 3D phantom beingmoved in rotation and/or translation between two successive images; andcalculating the intrinsic parameters of the imaging apparatus in itsfixed position by performing a calibration on the basis of the images ofthe 3D phantom.
 21. The method according to claim 4 comprisingdetermining the intrinsic parameters of the imaging apparatus by:placing a 3D phantom between the means for providing a radiation sourceand the means for receiving an image; acquiring a plurality of images ofthe 3D phantom in the determined fixed position of the imagingapparatus, the 3D phantom being moved in rotation and/or translationbetween two successive images; and calculating the intrinsic parametersof the imaging apparatus in its fixed position by performing acalibration on the basis of the images of the 3D phantom.
 22. The methodaccording to claim 5 comprising determining the intrinsic parameters ofthe imaging apparatus by: placing a 3D phantom between the means forproviding a radiation source and the means for receiving an image;acquiring a plurality of images of the 3D phantom in the determinedfixed position of the imaging apparatus, the 3D phantom being moved inrotation and/or translation between two successive images; andcalculating the intrinsic parameters of the imaging apparatus in itsfixed position by performing a calibration on the basis of the images ofthe 3D phantom.
 23. The method according to claim 9 comprisingdetermining the intrinsic parameters of the imaging apparatus by:placing a 3D phantom between the means for providing a radiation sourceand the means for receiving an image; acquiring a plurality of images ofthe 3D phantom in the determined fixed position of the imagingapparatus, the 3D phantom being moved in rotation and/or translationbetween two successive images; and calculating the intrinsic parametersof the imaging apparatus in its fixed position by performing acalibration on the basis of the images of the 3D phantom.
 24. The methodaccording to claim 14 comprising determining the intrinsic parameters ofthe imaging apparatus by: placing a 3D phantom between the means forproviding a radiation source and the means for receiving an image;acquiring a plurality of images of the 3D phantom in the determinedfixed position of the imaging apparatus, the 3D phantom being moved inrotation and/or translation between two successive images; andcalculating the intrinsic parameters of the imaging apparatus in itsfixed position by performing a calibration on the basis of the images ofthe 3D phantom.
 25. The method according to claim 1 comprising:adjusting the projection of a three-dimensionally reconstructed image ofthe body of the object onto two-dimensional radiographic images; anddisplaying the image.
 26. The method according to claim 2 comprising:adjusting the projection of a three-dimensionally reconstructed image ofthe body of the object onto two-dimensional radiographic images; anddisplaying the image.
 27. The method according to claim 3 comprising:adjusting the projection of a three-dimensionally reconstructed image ofthe body of the object onto two-dimensional radiographic images; anddisplaying the image.
 28. The method according to claim 4 comprising:adjusting the projection of a three-dimensionally reconstructed image ofthe body of the object onto two-dimensional radiographic images; anddisplaying the image.
 29. The method according to claim 5 comprising:adjusting the projection of a three-dimensionally reconstructed image ofthe body of the object onto two-dimensional radiographic images; anddisplaying the image.
 30. The method according to claim 9 comprising:adjusting the projection of a three-dimensionally reconstructed image ofthe body of the object onto two-dimensional radiographic images; anddisplaying the image.
 31. The method according to claim 14 comprising:adjusting the projection of a three-dimensionally reconstructed image ofthe body of the object onto two-dimensional radiographic images; anddisplaying the image.
 32. The method according to claim 29 comprising:adjusting the projection of a three-dimensionally reconstructed image ofthe body of the object onto two-dimensional radiographic images; anddisplaying the image.
 33. The method according to claim 1 comprising:repositioning two-dimensional radiographic image information in athree-dimensionally reconstructed image; and displaying the image. 34.The method according to claim 2 comprising: repositioningtwo-dimensional radiographic image information in a three-dimensionallyreconstructed image; and displaying the image.
 35. The method accordingto claim 3 comprising: repositioning two-dimensional radiographic imageinformation in a three-dimensionally reconstructed image; and displayingthe image.
 36. The method according to claim 4 comprising: repositioningtwo-dimensional radiographic image information in a three-dimensionallyreconstructed image; and displaying the image.
 37. The method accordingto claim 5 comprising: repositioning two-dimensional radiographic imageinformation in a three-dimensionally reconstructed image; and displayingthe image.
 38. The method according to claim 9 comprising: repositioningtwo-dimensional radiographic image information in a three-dimensionallyreconstructed image; and displaying the image.
 39. The method accordingto claim 14 comprising: repositioning two-dimensional radiographic imageinformation in a three-dimensionally reconstructed image; and displayingthe image.
 40. The method according to claim 29 comprising:repositioning two-dimensional radiographic image information in athree-dimensionally reconstructed image; and displaying the image. 41.The method according to claim 1 wherein the plurality of markers is atleast three.
 42. An imaging apparatus for determining thethree-dimensional movement of an object comprising: means for providinga radiation source; means for receiving an image; means for supportingthe object between the means for providing a radiation source and themeans for receiving an image; means for placing a plurality ofradio-opaque markers on a body of the object, the markers constituting afixed reference frame; means for operating, the means for operatingcausing the taking at least one first radiographic image of the objectfor a first determined fixed position of the imaging apparatus in thereference frame of the markers; the means for operating causing takingat least one second radiographic image of the object for a seconddetermined fixed position of the imaging apparatus in the referenceframe of the markers; the means for operating causing the determinationof a matrix of the three-dimensional movement of the object with respectto the means for providing a radiation source on the basis of thetwo-dimensional movements of the markers in the radiographic images, themeans for providing a radiation source constituting a fixed referenceframe; and means for visualizing the images.
 43. The apparatus accordingto claim 42 wherein: the means for operating determines a matrix of theintrinsic parameters of the imaging apparatus; the means for operatingdetermines a matrix of the extrinsic parameters of the imaging apparatusin the second position as a function of the matrix of the intrinsicparameters of the imaging apparatus; the means for operating determinesan inverse matrix of the extrinsic parameters of the imaging apparatusin its first position; and the means for operating determines a matrixcorresponding to the three-dimensional movement of the object as afunction of the inverse matrix of the extrinsic parameters of theimaging apparatus in its first position in the fixed reference frame ofthe markers and the matrix of the extrinsic parameters of the imagingapparatus in its second position in the fixed reference frame of themarkers.
 44. The apparatus according to claim 43 wherein the means foroperating determines the matrix of the extrinsic parameters of theimaging apparatus when taking the second radiographic image as afunction of the matrix of the intrinsic parameters of the imagingapparatus when taking the first radiographic image in the fixedreference frame of the markers.
 45. The apparatus according to claim 43wherein the means for operating determines the matrix of the extrinsicparameters of the imaging apparatus when taking the second radiographicimage by calculating the planar homography between the firstradiographic image of the markers and the second radiographic image ofthe markers, the markers forming a fixed reference frame.
 46. Theapparatus according to claim 42 wherein the means for operatingdetermines the matrix and the inverse matrix of the extrinsic parametersof the imaging apparatus in its first position on the basis of thematrix of the intrinsic parameters of the imaging apparatus.
 47. Theapparatus according to claim 43 wherein the means for operatingdetermines the matrix and the inverse matrix of the extrinsic parametersof the imaging apparatus in its first position on the basis of thematrix of the intrinsic parameters of the imaging apparatus.
 48. Theapparatus according to claim 44 wherein the means for operatingdetermines the matrix and the inverse matrix of the extrinsic parametersof the imaging apparatus in its first position on the basis of thematrix of the intrinsic parameters of the imaging apparatus.
 49. Theapparatus according to claim 45 wherein the means for operatingdetermines the matrix and the inverse matrix of the extrinsic parametersof the imaging apparatus in its first position on the basis of thematrix of the intrinsic parameters of the imaging apparatus.
 50. Theapparatus according to claim 42 wherein the markers are placed directlyon the body of the object.
 51. The apparatus according to claim 43wherein the markers are placed directly on the body of the object. 52.The apparatus according to claim 44 wherein the markers are placeddirectly on the body of the object.
 53. The apparatus according to claim45 wherein the markers are placed directly on the body of the object.54. The apparatus according to claim 42 comprising means for securingthe markers placed on the body of the object.
 55. The apparatusaccording to claim 43 comprising means for securing the markers placedon the body of the object.
 56. The apparatus according to claim 44comprising means for securing the markers placed on the body of theobject.
 57. The apparatus according to claim 45 comprising means forsecuring the markers placed on the body of the object.
 58. The apparatusaccording to claim 46 comprising means for securing the markers placedon the body of the object.
 59. The apparatus according to claim 43comprising determining the intrinsic parameters of the imaging apparatusby: a 3D phantom placed between the means for providing a radiationsource and the means for receiving an image; means for acquiring aplurality of images of the 3D phantom in the determined fixed positionof the imaging apparatus, the 3D phantom being moved in rotation and/ortranslation between two successive images; and the means for operatingcalculating the intrinsic parameters of the imaging apparatus in itsfixed position by performing a calibration on the basis of the images ofthe 3D phantom.
 60. The apparatus according to claim 44 comprisingdetermining the intrinsic parameters of the imaging apparatus by: a 3Dphantom placed between the means for providing a radiation source andthe means for receiving an image; means for acquiring a plurality ofimages of the 3D phantom in the determined fixed position of the imagingapparatus, the 3D phantom being moved in rotation and/or translationbetween two successive images; and the means for operating calculatingthe intrinsic parameters of the imaging apparatus in its fixed positionby performing a calibration on the basis of the images of the 3Dphantom.
 61. The apparatus according to claim 45 comprising determiningthe intrinsic parameters of the imaging apparatus by: a 3D phantomplaced between the means for providing a radiation source and the meansfor receiving an image; means for acquiring a plurality of images of the3D phantom in the determined fixed position of the imaging apparatus,the 3D phantom being moved in rotation and/or translation between twosuccessive images; and the means for operating calculating the intrinsicparameters of the imaging apparatus in its fixed position by performinga calibration on the basis of the images of the 3D phantom.
 62. Theapparatus according to claim 46 comprising determining the intrinsicparameters of the imaging apparatus by: a 3D phantom placed between themeans for providing a radiation source and the means for receiving animage; means for acquiring a plurality of images of the 3D phantom inthe determined fixed position of the imaging apparatus, the 3D phantombeing moved in rotation and/or translation between two successiveimages; and the means for operating calculating the intrinsic parametersof the imaging apparatus in its fixed position by performing acalibration on the basis of the images of the 3D phantom.
 63. Theapparatus according to claim 50 comprising determining the intrinsicparameters of the imaging apparatus by: a 3D phantom placed between themeans for providing a radiation source and the means for receiving animage; means for acquiring a plurality of images of the 3D phantom inthe determined fixed position of the imaging apparatus, the 3D phantombeing moved in rotation and/or translation between two successiveimages; and the means for operating calculating the intrinsic parametersof the imaging apparatus in its fixed position by performing acalibration on the basis of the images of the 3D phantom.
 64. Theapparatus according to claim 54 comprising determining the intrinsicparameters of the imaging apparatus by: a 3D phantom placed between themeans for providing a radiation source and the means for receiving animage; means for acquiring a plurality of images of the 3D phantom inthe determined fixed position of the imaging apparatus, the 3D phantombeing moved in rotation and/or translation between two successiveimages; and the means for operating calculating the intrinsic parametersof the imaging apparatus in its fixed position by performing acalibration on the basis of the images of the 3D phantom.
 65. Theapparatus according to claim 42 comprising: the means for operatingadjusting the projection of a three-dimensionally reconstructed image ofthe body of the object onto two-dimensional radiographic images; andmeans for visualizing displaying the image.
 66. The apparatus accordingto claim 43 comprising: the means for operating adjusting the projectionof a three-dimensionally reconstructed image of the body of the objectonto two-dimensional radiographic images; and means for visualizingdisplaying the image.
 67. The apparatus according to claim 44comprising: the means for operating adjusting the projection of athree-dimensionally reconstructed image of the body of the object ontotwo-dimensional radiographic images; and means for visualizingdisplaying the image.
 68. The apparatus according to claim 45comprising: the means for operating adjusting the projection of athree-dimensionally reconstructed image of the body of the object ontotwo-dimensional radiographic images; and means for visualizingdisplaying the image.
 69. The apparatus according to claim 46comprising: the means for operating adjusting the projection of athree-dimensionally reconstructed image of the body of the object ontotwo-dimensional radiographic images; and means for visualizingdisplaying the image.
 70. The apparatus according to claim 50comprising: the means for operating adjusting the projection of athree-dimensionally reconstructed image of the body of the object ontotwo-dimensional radiographic images; and means for visualizingdisplaying the image.
 71. The apparatus according to claim 54comprising: the means for operating adjusting the projection of athree-dimensionally reconstructed image of the body of the object ontotwo-dimensional radiographic images; and means for visualizingdisplaying the image.
 72. The apparatus according to claim 59comprising: the means for operating adjusting the projection of athree-dimensionally reconstructed image of the body of the object ontotwo-dimensional radiographic images; and means for visualizingdisplaying the image.
 73. The apparatus according to claim 42comprising: the means for operating repositioning two-dimensionalradiographic image information in a three-dimensionally reconstructedimage; and means for visualization displaying the image.
 74. Theapparatus according to claim 43 comprising: the means for operatingrepositioning two-dimensional radiographic image information in athree-dimensionally reconstructed image; and means for visualizationdisplaying the image.
 75. The apparatus according to claim 44comprising: the means for operating repositioning two-dimensionalradiographic image information in a three-dimensionally reconstructedimage; and means for visualization displaying the image.
 76. Theapparatus according to claim 45 comprising: the means for operatingrepositioning two-dimensional radiographic image information in athree-dimensionally reconstructed image; and means for visualizationdisplaying the image.
 77. The apparatus according to claim 46comprising: the means for operating repositioning two-dimensionalradiographic image information in a three-dimensionally reconstructedimage; and means for visualization displaying the image.
 78. Theapparatus according to claim 50 comprising: the means for operatingrepositioning two-dimensional radiographic image information in athree-dimensionally reconstructed image; and means for visualizationdisplaying the image.
 79. The apparatus according to claim 54comprising: the means for operating repositioning two-dimensionalradiographic image information in a three-dimensionally reconstructedimage; and means for visualization displaying the image.
 80. Theapparatus according to claim 59 comprising: the means for operatingrepositioning two-dimensional radiographic image information in athree-dimensionally reconstructed image; and means for visualizationdisplaying the image.
 81. The apparatus according to claim 42 whereinthe plurality of markers is at least three.
 82. A computer programcomprising program code means for implementing the method according toclaim 1 when the program runs on a computer, the program being disposedin a computer readable medium.
 83. A computer program product comprisinga computer useable medium having computer readable program code meansembodied in the medium, the computer readable program code meansimplementing the method according to claim
 1. 84. An article ofmanufacture for use with a computer system, the article of manufacturecomprising a computer readable medium having computer readable programcode means embodied in the medium, the program code means implementingthe method according to claim
 1. 85. A program storage device readableby a machine tangibly embodying a program of instructions executable bythe machine to perform the method according to claim 1.